To determine for which store location 68% of the data falls between \[tex]$19,371.18 and \$[/tex]22,295.48, we will calculate the interval for each location using the mean and the standard deviation (SD). This interval is given by mean ± 1 SD.
1. Location A:
- Mean: \[tex]$23,124.70
- SD: \$[/tex]1,553.43
- Interval: [tex]\(23,124.70 - 1,553.43\)[/tex] to [tex]\(23,124.70 + 1,553.43\)[/tex]
[tex]\[
= 21,571.27 \text{ to } 24,678.13
\][/tex]
2. Location B:
- Mean: \[tex]$24,842.18
- SD: \$[/tex]1,617.20
- Interval: [tex]\(24,842.18 - 1,617.20\)[/tex] to [tex]\(24,842.18 + 1,617.20\)[/tex]
[tex]\[
= 23,224.98 \text{ to } 26,459.38
\][/tex]
3. Location C:
- Mean: \[tex]$20,833.33
- SD: \$[/tex]1,462.15
- Interval: [tex]\(20,833.33 - 1,462.15\)[/tex] to [tex]\(20,833.33 + 1,462.15\)[/tex]
[tex]\[
= 19,371.18 \text{ to } 22,295.48
\][/tex]
4. Location D:
- Mean: \[tex]$21,432.82
- SD: \$[/tex]1,512.10
- Interval: [tex]\(21,432.82 - 1,512.10\)[/tex] to [tex]\(21,432.82 + 1,512.10\)[/tex]
[tex]\[
= 19,920.72 \text{ to } 22,944.92
\][/tex]
Now, we examine if the interval between \[tex]$19,371.18 and \$[/tex]22,295.48 lies within the calculated intervals for each location.
- Location A: The interval is \[tex]$21,571.27 to \$[/tex]24,678.13. The given range does not fall within this interval.
- Location B: The interval is \[tex]$23,224.98 to \$[/tex]26,459.38. The given range does not fall within this interval.
- Location C: The interval is \[tex]$19,371.18 to \$[/tex]22,295.48. The given range exactly matches this interval.
- Location D: The interval is \[tex]$19,920.72 to \$[/tex]22,944.92. The given range does not fall within this interval.
Therefore, the correct answer is:
C. Location C
